Basic example of the RSA algorithm in R

RSA.R

# RSA example 
# 
# Bastiaan Quast
# International Telecommunication Union
# bastiaan.quast@itu.int

# Two people - Alice and Bob - want to communicate privately
# A third person Eve wants to read the private communication
Alice = list()
Bob   = list()

# Bob generates a message 'hi'
# we can represent this numberically as 89 (h is the 8th letter of the alphabet, i the 9th)
Bob$m = 89

# Alice generates two random prime numbers
Alice$p = 53
Alice$q = 59
Alice$n  = Alice$p * Alice$q

# calculate Phi(n)
Alice$Phi_n = (Alice$p-1)*(Alice$q-1)

# Alice choses an exponent
Alice$e = 3

# Alice calculates the private part of the key
Alice$d = (2*Alice$Phi_n + 1) / 3

# publish the public key (here by putting the global environment)
n = Alice$n
e = Alice$e

# Bob encrypts his message
c = Bob$m^e %% n

# install and load the GNU Multiple Percision Arithmetic R package 
install.packages('gmp')
library(gmp)

# Alice decrypts Bob's message
Alice$cpowd <- as.bigz(c)^Alice$d
Alice$m = Alice$cpowd %% n
print(Alice$m)